About the Long Multiplication Calculator
This long multiplication calculator multiplies two numbers using the standard column method and shows the full working: the numbers lined up, one partial product for each digit of the bottom number (with the placeholder zeros), the carries in each row, and the final addition. For 347 × 26 you see 347 × 6 = 2,082 and 347 × 20 = 6,940, which add up to 9,022.
It is made for students learning multi-digit multiplication in grades 4–6, parents checking homework, and teachers who want a quick answer key with the steps laid out the way they are taught. Decimals are handled the classroom way too: multiply as whole numbers, then count the decimal places in both factors to place the point in the answer.
Numbers up to 30 digits each are multiplied exactly with integer arithmetic, so even very large products have no rounding. Negative numbers follow the usual sign rule — the product is negative when exactly one factor is negative.
How to use the long multiplication calculator
- 1Enter the top number and the bottom number (whole numbers or decimals).
- 2Read the product at the top of the results.
- 3Follow the working: one partial product per digit of the bottom number, shifted by place value.
- 4Check the carries column in the table if you are learning the method.
- 5For decimals, see how the decimal places are counted to place the point.
Formula and method
Long multiplication uses the distributive law. The bottom number is split into its digits by place value — 26 = 6 + 20 — and the top number is multiplied by each part separately: 347 × 6 and 347 × 20. Multiplying by a tens digit is done by multiplying by the digit and writing a placeholder zero, by a hundreds digit with two zeros, and so on. Adding these partial products gives the answer.
Within each row, multiply the top number digit by digit from right to left, writing the units digit of each small product and carrying the tens digit into the next column. For decimals, ignore the points, multiply the whole numbers, then put the decimal point in the answer so that it has as many decimal places as both factors combined.
- a
- Top number (multiplicand)
- bᵢ
- Digit of the bottom number in place i (ones, tens, …)
- 10ⁱ
- Place value — shown as placeholder zeros
Worked examples
347 × 26
347 × 6 = 2,082 (7 × 6 = 42, write 2 carry 4; 4 × 6 + 4 = 28, write 8 carry 2; 3 × 6 + 2 = 20). 347 × 20 = 6,940. Then 2,082 + 6,940 = 9,022.
1234 × 5678
The four partial products are 1234 × 8 = 9,872, 1234 × 70 = 86,380, 1234 × 600 = 740,400 and 1234 × 5000 = 6,170,000. Their sum is 7,006,652.
Decimals: 3.25 × 1.4
Multiply 325 × 14 = 1,300 + 3,250 = 4,550. The factors have 2 + 1 = 3 decimal places, so the answer is 4.550 = 4.55.
Negative factor: −12 × 15
12 × 15 = 60 + 120 = 180. Exactly one factor is negative, so the product is −180.
Big numbers: 123456789 × 987654321
Nine partial products are added exactly with integer arithmetic, giving 121,932,631,112,635,269 — too long for an ordinary calculator display to show in full.
Frequently asked questions
How do you do long multiplication?+
Write the larger number on top. Multiply it by the ones digit of the bottom number, then by the tens digit (writing one zero first), then the hundreds digit (two zeros), and so on. Finally add all the rows together.
Why do you add a zero in the second row?+
The second digit of the bottom number is in the tens place, so you are really multiplying by a multiple of ten — for 26 that is 20, not 2. The placeholder zero shifts the row one place left to account for that.
How do you multiply decimals using long multiplication?+
Ignore the decimal points and multiply as whole numbers. Then count the total decimal places in both factors and place the point that many digits from the right of the answer. For 2.5 × 0.13, 25 × 13 = 325 and there are 3 decimal places, giving 0.325.
What is the difference between long multiplication and the grid method?+
Both split numbers by place value. The grid (box) method writes every digit-by-digit product in a table and adds them all, while long multiplication combines one whole row per digit of the bottom number, using carries. They give the same answer.
How can I check a long multiplication answer?+
Round both numbers to one significant figure and multiply to estimate, or swap the order of the factors and redo it. Casting out nines (comparing digital roots) is another quick check that catches most slips.